A mobile robot for toxic waste cleanup is shown in Figure DP9.1 (a) [23]. The closed-loop speed control is represented by Figure 9.1 with H(s) = 1. The Nichols chart in Figure DP9.1 (b) shows the plot of Gc(jω) G(jω)/K versus ω. The value of the frequency at the points indicated is recorded in the following table:
(a) Determine the gain and phase margins of the closed-loop system when K =1. (b) Determine the resonant peak in dB and the resonant frequency for K =-1, (c) Determine the system bandwidth and estimate the settling time (with a 2% criterion) and percent overshoot of this system for a step input. (d) Determine the appropriate gain K so that the overshoot to a step input is 30%, and estimate the settling time of the system.
